National Examinations Board Grade 12 Business Mathematics — Grade Increment (Supplementary) 2080 (2023) (Set B)

National Examinations Board · Business Mathematics (Grade 12) · 2080 (2023) BS · Grade Increment (Supplementary) Examination — 22 questions — a free old question paper on Goodone.club’s exam-paper archive.

  1. If A = [[1,0],[0,1]] and B = [[3,2],[1,2]], then AB is (A) [[3,2],[1,2]] (B) [[2,1],[2,3]] (C) [[2,3],[2,1]] (D) [[1,3],[2,1]] [1 marks]
  2. The cost of 3 chairs, 2 tables and 1 desk is Rs. 97,000. The cost of 2 chairs, 1 table and 3 desks is Rs. 86,000, and the cost of 1 chair, 3 tables and 2 desks is Rs. 99,000. Find the cost of a chair, a desk and a table by using the matrix method. [5] [5 marks]
  3. A company manufactures different types of electrical appliances and has been using radio to advertise its products. The following table shows the amount of radio time (x, in minutes) and the number of electrical appliances sold (y) over the last six days: x = 20, 28, 42, 31, 45, 24; y = 25, 14, 25, 26, 16, 22. (a) Calculate the Karl Pearson's coefficient of correlation. [4] (b) Estimate the sales (number of electrical appliances) when the amount of radio time (x) is 50. [4] [8 marks]
  4. If AB is an identity matrix such that the leading diagonal elements of A are the roots of x²−2x+1 = 0 and the order of A is 2×2, then B is (A) [[0,1],[1,0]] (B) [[0,−1],[−1,0]] (C) [[−1,0],[0,−1]] (D) [[1,0],[0,1]] [1 marks]
  5. (a) Solve the following system of equations using the Gauss elimination method: 3x+y+z = 5, x−4y+z = −2, x+y−3z = −1. [3] (b) Prove that, without expanding, |bc a a²; ca b b²; ab c c²| = |1 a² a³; 1 b² b³; 1 c² c³|. [2] [5 marks]
  6. The compound interest on a certain sum at a certain rate is Rs. 204 in 2 years, and the simple interest at the same rate is Rs. 300 in 3 years. (a) Find the sum and rate of interest. (b) If the rate of interest is doubled and the principal is the same, in how many years will the amount become Rs. 3149.28? [8 marks]
  7. If [[0, x+2],[5, 0]] is a skew-symmetric matrix for positive x+2, then x is (A) −3 (B) 3 (C) −7 (D) 7 [1 marks]
  8. The total cost function and demand function of a commodity are 2Q−Q² and Q−3 respectively. (a) Write the revenue function in terms of Q. [1] (b) Write the related profit function. [1] (c) Name the marginal revenue function. [1] (d) What is the profit at Q = 2? [2] [5 marks]
  9. The demand and supply functions in a competitive market are Qd = 500 − 5p and Qs = 20p − 40 respectively. The initial price P₀ is Rs. 100. Derive a function for the time path P and use it to predict the price in time period 5, given that the price adjusts in proportion to excess demand at the rate dp/dt = 0.02(Qd − Qs). How many time periods would you have to wait for the price to drop by Rs. 60? Comment on the stability of this market. [8 marks]
  10. The point of inflection of the function y = x⁴ is (A) 0 (B) 1 (C) −1 (D) No point of inflection [1 marks]
  11. (a) Find the area bounded by the curves y = x²+2 and y = x. [3] (b) Solve the differential equation dy/dx + y = eˣ. [2] [5 marks]
  12. The solution of the differential equation y dx + x dy = 0 is (A) x+y = c (B) x−y = c (C) xy = c (D) x = yc [1 marks]
  13. The demand and supply functions of a commodity are Pd = 113 − x² and Ps = (x+1)² in a perfect competition. Find the consumer surplus and producer surplus at the market equilibrium prices. [5] [5 marks]
  14. The product of three numbers in G.P. is 64. Which one of the following is the second term of the G.P.? (A) 8 (B) 4 (C) −4 (D) −8 [1 marks]
  15. Solve the following linear programming problem by the simplex method to maximize P = 12x + 5y subject to the constraints 4x + y ≤ 3, 3x + y ≤ 1, x ≥ 0, y ≥ 0. [5] [5 marks]
  16. If the net return after 1 year is Rs. 5000 and the initial investment is Rs. 40,000, then the Internal Rate of Return (IRR) is (A) 10% (B) 12.5% (C) 15% (D) 20% [1 marks]
  17. In a data, x̄, Md, Mo and σ represent the mean, median, mode and standard deviation respectively. (a) Write two different formulae of Karl Pearson's skewness. [2] (b) Write the relation between mean, median and mode of the data. [1] (c) Write the coefficient of variation in terms of σ and x̄. [1] (d) State the condition of positive skewness in terms of the above symbols. [1] [5 marks]
  18. The present value of an immediate annuity of Rs. 1200 payable for 5 years at compound interest at the rate of 10% p.a. is (A) 12000[1−(1.1)⁵] (B) 12000[1−(1.1)⁻⁵] (C) 12000[(1.1)⁵−1] (D) 12000[(1.1)⁻⁵−1] [1 marks]
  19. A box has a total of 15 golf gloves of the same size and shape. The ratio of left-hand gloves to right-hand gloves is 2:1. If two gloves are randomly selected from the box without replacement, what is the probability that (a) both gloves are left-handed? (b) one is right-handed and one is left-handed? (c) What would be the probability of getting both gloves right-handed if the process of drawing is different from that in cases (a) and (b)? [5 marks]
  20. Every linear programming problem (LPP) is associated with another LPP that is (A) surplus (B) primal (C) slack (D) dual [1 marks]
  21. Which of the following is the condition for negative skewness in data? (A) mean < median < mode (B) mean > median > mode (C) mean = median = mode (D) median > mean > mode [1 marks]
  22. (p+q)ⁿ is a binomial distribution with parameters n and p. What is the variance of the distribution? (A) npq (B) np (C) nq (D) √(npq) [1 marks]